Right triangles

When the spectral loci are plotted in this manner, with adjustments to make the XYZ triangle right-angled, the chromaticity diagram in Fig. 26.14 is obtained. The wavelengths corresponding with various positions on the curve are marked in numerals. 

Fig. 4. Same values of dynamic surface tension as in Fig. 3, panel e) (circles, left axis scale), together with the synchronous values of surface area (small triangles, right axis scale)...

Fig. 30. Curie points, (circles), spin-reorientation temperatures, (diamonds) and saturation magnetic moments at 1.5 K (triangles, right-hand scale) versus V concentration x for NdFe,2, V, (H. Yang et al. 1993).

Hypotenuse of Sides of right triangle right triangle... 

Figure 9.10 SdFFF fractogmms obtained for a 47% v/v F66E emulsion, a 47% v/v PFHB emulsion, and an equivolume mixture of the two, 10 minutes after mixing. Diffusional mass transfer occurs from the PFHB droplets, which have moderate water solubility, to the F66E droplets, which have low water solubility. The inset shows that equivolume ratios of the two fluorocarbons (as determined by gas chromatography) are found across the entire particle size distribution (triangles, right ordinate where Vf66e volume fraction of F66E in the droplets) for the mixed emulsion sample. The dashed line represents the predicted composition for the case where all of the PFHB has diffused into the F66E droplets (i.e. a 50/50 bulk ratio)...

Figure 13.15 Density of states (DOS) normalized by frequency versus frequency as a function of packing fraction. The boson peak decreases with increasing volume fraction. The boson peak frequency (circles, left) and inverse peak height of DOS (triangles, right) versus c ). (Reprinted with permission from Chen, K., Ellenbroek, W. G., Zhang, Z. et al.. Low-frequency vibrations of soft colloidal glasses, Phys. Rev. Lett, 105, 025501, 2010. Copyright 2010 by the American Physical Society.)...

A second notion is that each atom i.s described twice - in a column and in a row. Matrices in which all elements are shown twice are called redundant. A non-redun-dant matrix contains each element only once (e,g., only the top right or bottom left triangle of the matrix, as can be seen later). 

Figure 2-17. a) The redundanl bond malrix of ethanal with ihe zero values omitted, b) It can be compressed by reduction to the top right triangle, c) Omitting the hydrogen atoms provides the simplest non-redundant matrix representation. 

The polynomial expansion used in this equation does not include all of the temis of a complete quadratic expansion (i.e. six terms corresponding to p = 2 in the Pascal triangle) and, therefore, the four-node rectangular element shown in Figure 2.8 is not a quadratic element. The right-hand side of Equation (2.15) can, however, be written as the product of two first-order polynomials in temis of X and y variables as... 

After obtaining the described decomposition the set of equations can be readily solved. This is because all of the information required for transfonnation of the coefficient matrix to an upper triangular fonn is essentially recorded in the lower triangle. Therefore modification of the right-hand side is quite straightforward and can be achieved using the lower triangular matrix as... 

Right Triangle (Fig. 3-44) Given one side and any acute angle Ot or any two sides, the remaining parts can be obtained from the following formulas ... 

The simplest form of ternary RCM, as exemplified for the ideal normal-paraffin system of pentane-hexane-heptane, is illustrated in Fig. 13-58 7, using a right-triangle diagram. Maps for all other non-azeotropic ternary mixtures are qiiahtatively similar. Each of the infinite number of possible residue curves originates at the pentane vertex, travels toward and then away from the hexane vertex, and terminates at the heptane vertex. 

Figure 3 Flow of a distance geometry calculation. On the left is shown the development of the data on the right, the operations, d , is the distance between atoms / and j Z. , and Ujj are lower and upper bounds on the distance Z. and ZZj, are the smoothed bounds after application of the triangle inequality is the distance between atom / and the geometric center N is the number of atoms (Mj,) is the metric matrix is the positional vector of atom / 2, is the first eigenvector of (M ,) with eigenvalue Xf,. V , r- , and ate the y-, and -coordinates of atom /. (1-5 correspond to the numbered list on pg. 258.)...

Eor noncircular apertures, the equivalent hydraulic diameter should be used. Eor crimped metal ribbon elements, the equivalent hydraulic diameter of a right isosceles triangle is 0.83 times the crimp height, and the thickness (width) should be at least 0.5 inches (EISE 1980). 

For definitions of trigonometric functions, see Trigonometry. ) Right triangle (Figure 1-1)... 

Figure 54.5 Common right triangle and simplified alignment-measuring apparatus...

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